a) The probability of having exactly 3 aces in a 7-card hand is approximately 0.0058.
b) The probability of having exactly 3 of a kind in a 7-card hand is approximately 0.0211.
The probability of drawing a specific card from a deck of 52 cards is 1/52.
a) To find the probability of having exactly 3 aces in a 7-card hand, we can use the binomial distribution:
P(exactly 3 aces) = (number of ways to choose 3 aces from 4 aces) * (number of ways to choose 4 non-aces from 48 non-aces) / (number of ways to choose 7 cards from 52 cards)
= (4C3 * 48C4) / 52C7
= (4 * 194580) / 133784560
= 0.005755
Therefore, the probability of having exactly 3 aces in a 7-card hand is approximately 0.0058.
b) To find the probability of having exactly 3 of a kind in a 7-card hand, we can use the following steps:
Choose the rank of the 3 of a kind (13 options)Choose 3 suits for the chosen rank (4C3 options)Choose 4 ranks from the remaining 12 ranks (12C4 options)Choose 1 suit for each of the 4 remaining ranks (4 options each)Multiply the number of options from each step to get the total number of hands with exactly 3 of a kind.The total number of 7-card hands is 52C7 = 133,784,560.
Therefore, the probability of having exactly 3 of a kind in a 7-card hand is:
P(exactly 3 of a kind) = (13 * 4C3 * 12C4 * 4^4) / 133784560
= (13 * 4 * 495 * 256) / 133784560
= 0.02113
Therefore, the probability of having exactly 3 of a kind in a 7-card hand is approximately 0.0211.
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Translation problems, please help!!
The rule to describe the translation 5 units left and 10 units up is given as (x, y) ⇒ (x -5, y + 10).
What is translation?A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.
Given that the translation is to the left by 5 units.
When the graph shifts to the left by 5 units the graph shifts on the x-axis, and this is represented as follows:
(x, y) ⇒ (x - 5, y)
When the graph is translated up by 10 units the graph shifts on the y-axis and this is represented as follows:
(x , y) ⇒ (x -5, y + 10).
Hence, The rule to describe the translation 5 units left and 10 units up is given as (x, y) ⇒ (x -5, y + 10).
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What conclusions can you make about the figure?
Note that the conclusions that can be made about the above-given figure is that :
Δ PQR ~ ΔPST by the AA Similarity Theorem.
∠PQR ≅ ∠ PST also by the AA Similarity Theorem.
What is the by the AA Similarity Theorem?According to the AA similarity theorem, if two triangles of one triangle are equivalent to two angles of another triangle, then the two triangles are similar. As a result of comparable angles in each triangle, the two triangles are identical.
The three similarity rules are as follows:
AA. : Two comparable angle pairs are equal.
SSS. : Three comparable pairs of sides are proportionate.
SAS. : Two matching side pairs are proportionate, and their corresponding angles are equal.
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Help with question 3
The solution is [tex](27^2)^{ 1/5}[/tex] express as [tex]145 \frac{4}{5}[/tex] in simplest radical form.
How to calculate simplest radical form?A radical in mathematics is the opposite of an exponent, which is denoted by the symbol "√" and is also referred to as the root. It can either be a square root or a cube root, and the number before the symbol or radical is regarded as an index number or degree. This number cancels the radical and is represented as a whole number by an exponent.
step1:
extract form
27² =729
729/5= decimal form=145.8
step 2:
729/5=145.8
mixed form:
[tex]145 \dfrac{4}{5}[/tex]
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Which transformation is similar but not congruent to the original figure?A.dilationB.rotationC.reflectionD.translation
Dilation and rotation is a series of transformations that would produce a figure that is similar to the original figure but not congruent with it.
Transformation of dilation and rotation:
Rigid transformations, such as rotations, reflections, and translations, do not alter the size or shape of a figure; rather, they only move it. The congruence is preserved by these hard changes.
However, because dilation alters a shape's size, they are not hard transformations. The ratio of matching sides would be equal to the scale factor used in the dilatation; the form would remain the same, just the size would vary. This would provide us with a comparable but in congruent value.
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Complete each problem and show your work Diameter: 12,756 km
Diameter: 12,756 km Radius: 15.25in Circumference: 7in Circumference: 25.92cm
C = C = D = R =
A = A = A = A =
The area of the circle would be 127731695.76 Km².
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the diameter of the circle.
The diameter is -
{d} = 12756 Km
We can write the radius as -
r = {d}/2 = 6378 Km
We can write the area as -
A = 3.14 x 6378 Km x 6378 Km
A = 127731695.76 Km²
Therefore, the area of the circle would be 127731695.76 Km².
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Which of the following are quadratic equations? `(i)3x^2-5x+9=x^2-7x+3` (ii) `x+1/x=1` (iii) `x^2-3x=0`
Option (i) , (ii) and (iii) all represents quadratic equations as all of them is of degree 2 and coefficient of degree 2 is non-zero.
What is quadratic equation?Having the form a[tex]x^2[/tex] + bx + c = 0, quadratic equations are 2nd degree algebraic expressions. The meaning of the term "quad," is square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.
Option i
3x^2-5x+9=x^2-7x+3
so the coefficent of degree 2 is 3-1 which is 2 which is non - zero value so this expression is a quadratic equation.
Option ii
x+ [tex]\frac{1}{x}[/tex] =1
=> [tex]x^2[/tex] -x +1=0
so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.
Option iii
[tex]x^2[/tex] -3x=0
so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.
so all the 3 option represents a quadratic equation.
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Find the area and perimeter of a triangle with ide length of 4 1/5 inche,and 4 2/7 inche
The perimeter of a triangle is about 18.77 inch and the area of a triangle is about 18 [tex]inch^{2}[/tex] .
What is triangle ?
A triangle is a three-sided polygon with three straight sides. The three sides of a triangle are called edges, and the three angles of a triangle are called vertices. The sum of the three angles of a triangle is always 180 degrees.
Have given ,
length of triangle [tex]4\frac{1}{5} ,4\frac{2}{7}[/tex],
perimeter of a triangle = [tex]4\frac{1}{5} +2*4\frac{2}{7}+6[/tex] = 18.77 inch.
Area of a triangle = [tex]\frac{1}{2}*2*4\frac{1}{5}*4\frac{2}{7}[/tex]
⇒ 18 [tex]inch^{2}[/tex].
Hence , The perimeter of a triangle is about 18.77 inch and the area of a triangle is about 18 [tex]inch^{2}[/tex] .
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An 9009h2
7 There are almost 40 thousand fourth graders in Mississippi and almost 400 thousand fourth graders in
Texas. There are almost 4 million fourth graders in the United States.
We write 4 million as 4,000,000. How many times more fourth graders are there in Texas than in
Mississippi? How many times more fourth graders are there in the United States than in Texas? Use the
approximate populations listed above to solve.
There are about 4 thousand fourth graders in Washington, D.C. How many times more fourth graders are
there in the United States than in Washington, D.C.?
There are about 1,000 times as many fourth graders in the US as there are in Washington DC.
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
We write 4 thousand as 4,000
We write 40 thousand as 40,000
We write 400 thousand as 400,000
The value of each place is ten times the value of the place immediately to the right.
So:
40,000 is 10 times 4,000
400,000 is 10 times 40,000.
4,000,000 is 10 times 400,000.
Thus, 400,000 = 10 *40,000, and there are about 10 times as many fourth graders in Texas as there are in Mississippi.
Also, 4,000,000 = 10* 400,000, and there are about 10 times as many fourth graders in the US as there are in Texas.
Finally, to go from 4,000 to 4,000,000, we have to multiply by 10 three times. We see that
10*10*10 = 10 * 100 = 1000
Hence, there are about 1,000 times as many fourth graders in the US as there are in Washington DC.
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You pick a card at random. 4 5 6 7 What is P(less than 7)? Write your answer as a percentage
The probability P(less than 7) is 3/4.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
For the given situation,
The cards are numbered as s = {4,5,6,7}
n(s)=4
The event is probability of picking the cards less than 7
Cards less than 7,
e=4, 5, 6
n(e)=3
Probability of picking the card is given by p(e)=n(e)/n(s)
p(less than 7)=3/4
Hence, the probability P(less than 7) is 3/4.
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Which type of Wave has the most energy
Answer: Gamma rays
Step-by-step explanation: Gamma rays have the highest energies and shortest wavelengths on the electromagnetic spectrum.
What is the answer to √32^x=4? Solve for x.
Answer: 22.627
Step-by-step explanation:
if I did this right, it would be the reverse equation:
4 * the [tex]\sqrt32\\[/tex]
i apologize if I'm wrong
a) What sum amounts to Rs. 3,600 in 2 years at the rate of 10% p.a.
At a 10% annual growth rate, the cash equals Rs. 3,600 in two years. Rs. 3960.
What does total principal amount mean?The principal is the sum you borrowed and are required to repay, while the interest is what you pay. For the majority of borrowers, the total monthly payment you make to your mortgage company includes additional expenses like homeowners taxes and homeowner's insurance that may be placed in an escrow account.
According to the given information:
here principal(P)=3600, R=10%, n= 2 year
amount A=p(1+R/100)ⁿ
3600(1+10/100)²
3600*11/10
=3690
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What is the property of substitution?
The property of substitution states that if an expression is equal to a second expression, then replacing a part of one expression with the corresponding part of the other expression will also result in an equivalent expression.
Exploring the Property of Substitution in AlgebraThe property of substitution is a fundamental concept in algebra that allows us to manipulate equations and expressions. This property states that if two expressions are equivalent, then replacing a part of one expression with the corresponding part of the other expression will also result in an equivalent expression. This allows us to make substitutions in equations and expressions in order to find solutions. This property is essential when solving equations, since it allows us to replace unknown variables with known values, enabling us to find the solution. It is also important when simplifying expressions, since it allows us to replace parts of the expression with simpler parts in order to find the simplified form.
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Find the midpoint of segment EF (10,-7) and (8,5)
The midpoint of segment EF whose endpoints area at; (10,-7) and (8,5)as required is; (9, -1).
What is the midpoint of.tge segment EF?It follows from the task content that the midpoint of the segment EF is to be determined.
Since the given endpoints of the segment are: (10,-7) and (8,5) and it follows from the midpoint formula that;
Midpoint, M = ( (x₂ + x₁)/2 , (y₂ + y₁) /2 )
On this note, the midpoint of the segment EF as required is;
M = ( (10+8)/2 , (-7 + 5)/2 )
M = (9, -1)
Ultimately, the midpoint of the segment EF is; (9, -1).
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Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
A) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
B) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
C) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
What is the quotient of 3 divided by 8?
The quotient of 3÷8 is 0.375
The number 3 is called the numerator or dividend, and the number 8 is called the denominator or divisor.
The quotient of 3 and 8, the ratio of 3 and 8, as well as the fraction of 3 and 8 all mean (almost) the same:
3 divided by 8, often written as 3/8.
The result of 3/8 is a terminating decimal with 3 digits to the right of the decimal point.
3 divided by 8 in decimal = 0.375
3 divided by 8 in fraction = 3/8
3 divided by 8 in percentage = 37.5%
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Lian wants to place wood flooring in his rectangular-shaped laundry room with the dimensions
show below. How much flooring does Lian need?
The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.
what is rectangle ?A rectangle is a polygon with four right angles in Euclidean plane geometry. You may also refer to it as an equiangular quadrilateral, meaning that all of its degrees are comparable. A straight angle could also be present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90-degree vertices with equal parallel sides make up a quadrilateral with the outline of a rectangle. As a result, it's also known as a georeferencing rectangle. A rectangle is also referred to as a parallelogram since its opposite sides remain parallel and equal.
given
are of floor = 12 * 12
= 144 ft2
The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.
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how old am i if 400 reduced byy one half must subtracted from 257
You are 57 years old if 400 reduced by one half must subtracted from 257 is your age in the given arithmetic problem.
What is arithmetic?Mathematical arithmetic, which includes operations on numbers, is its foundation. Addition, subtraction, multiplication, and division are among these operations. The foundation of the subject "Maths" is laid by one of the crucial branches of mathematics: arithmetic.
Despite the fact that the subject involves numerous other modified operations, addition, subtraction, division, and multiplication are the three basic operations under the heading of arithmetic.
Let your age be x
[tex]$x=257-400\frac{1}{2}[/tex]
x = 257 - 200
x = 57
Hence, your age is 57 years old.
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34. Apply Math Models Olivia makes and sells
bracelets and necklaces. She can make up to
60 pieces per week. Write and graph a system
of inequalities that shows the combination of
bracelets and necklaces that she can make if
she wants to sell at least 30 items per week.
If necklaces sell for $8 each and bracelets sell
for $5 each, what is the most money she can
make in a week? Explain.
The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).
what is unitary method ?The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.
given
Assume that y is the number of necklaces and x is the number of bracelets.
Up to (less than or equal to) 60 pieces (bracelets and necklaces) can be produced by Olivia each week:
x+ y ≤60
Up to (less than or equal to) 40 bracelets can be made by Olivia each week:
x≤40(2)
Up to (less than or equal to) 40 necklaces can be created by Olivia each week.
y≤40(3)
Olivia aims to sell at least 30 products per week, preferably more.
x+y≥30(4)
It is possible to write x+y60 as yx+60 with a boundary of y=x+60. Since is used, we shade below the line and draw the line as solid. (red)
The vertical boundary of x40 is defined by x=40. Because is employed,, after which we darken the line's left side and draw the line as solid. (orange)
The horizontal boundary of y40 is defined by y=40. Because is utilized, we shade below the line and draw a solid line over it. (green)
The expression x+y30 can be written as yx+30 has a limit of y=x+30.
Because is utilized, we shade above the line and draw the line as a solid. (blue)
The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).
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y-9+y-4 combining like terms (middle school)
By combining the like terms from the given expression we get 2y-13
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
Given ,
The expression ,
=y-9+y-4
=y+y-(9+4)
=2y-13
Hence , By combining the like terms from the given expression we get 2y-13.
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Is 8 a factor of 63q + 15
Answer:
because it has many factors other than 1 and 18
Solve the system of equations using elimination: x-3y=-14x−3y=−14 and x-7y=-26x−7y=−26.
Answer:
2x - 10y = - 40
Step-by-step explanation:
x - 3y = -14
x - 7y = -26
2x - 10y = - 40
I'LL DO ANYTHING FOR THE ANSWER!!!
Answer: 1. 55 sq inches
Step-by-step explanation:
add me and mark me brainlyest pls
Answer:
15.5 inches
Step-by-step explanation:
10cm = 3.93701 inches
3.93701 x 3.93701 = 15.50004774
15.50004774 to the nearest tenth is 15.5
Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too.
Is this argument inductive or deductive?
If it is inductive, is it strong or weak?
If it is deductive, is it valid or invalid?
Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too which means that the argument is inductive and it is a weak one.
What is an Inductive argument?This is a type of argument which is characterized by the arguer believing that the truth of the premises provides only good reasons to believe the conclusion is probably true.
In this scenario since Annie liked the author's previous books and the new one had great reviews then it is probably true that she would also like it and it is a weak one because assuming the premises are true,then it is probable for the conclusion to be false.
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Which of the following is a solution of the equation 2x 3y 13?
Step-by-step explanation:
Given equations are
2x+3y=13 ....(1)
4x+y=11 .....(2)
multiply the equation (2) by 3, we get
⇒12x+3y=33 .....(3)
Subtract equation (1) from (3) to eliminate y, we get
12x+3y=33
2x+3y=13
− − −
10x=20
⇒x=2
Put this value in equation (1), we get
⇒2(2)+3y=13
⇒4+3y=13
⇒3y=9
⇒y=3
∴ the solution is x=2,y=3.
What is the solution to the system of linear equations x 3y =- 2?
The solution to the system of linear equations x 3y =- 2 is (x, y) = (6, -2).
The solution to the system of linear equations x 3y =- 2 can be found by using a method such as substitution or elimination.
One possible method is substitution, where we solve one equation for one variable in terms of the other, and then substitute that expression into the other equation.
For example, we can solve the equation x + 3y = -2 for x in terms of y: x = -3y - 2. Then we can substitute this expression into the second equation: -3y - 2 + 3y = -2, which simplifies to y = -2.
Then we can substitute this value back into the first equation to find x: x = -3(-2) - 2 = 6.
So the solution to the system of linear equations x 3y =- 2 is (x, y) = (6, -2).
In conclusion, The system of linear equations x + 3y = -2 can be solved by using the method of substitution. By solving one equation for one variable in terms of the other, and substituting that expression into the other equation, we find that the solution to the system is (x, y) = (6, -2).
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What is a 1/3 scale factor?
A 1/3 scale factor is a constant of dilation that is used to change the size of a figure by a factor of 1/3. A dilation is a transformation that changes the size of a figure while preserving its shape.
In a dilation, the scale factor is multiplied by the coordinates of each point on the figure to determine the new coordinates of the dilated figure. If the scale factor is 1/3, then the coordinates of each point on the figure will be multiplied by 1/3, meaning that each point on the figure will be moved one-third as far from the origin as it was before the dilation.
The result of this is that the dilated figure will be smaller than the original figure and will have a scale factor of 1/3. It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.
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Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
please help me please
Michael and Ashley bought same amount of turkey and ham.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Michael and Ashley each buy x pounds of turkey and y pounds of ham.
Michael purchased from store A.
Cost of turkey per pound at store A = $3
Cost of ham per pound at store A = $4
Michael spends $18 at store A.
3x + 4y = 18
Ashley purchased from store B.
Cost of turkey per pound at store B = $4.50
Cost of ham per pound at store B = $6
Ashley spends $27 at store B.
4.5x + 6y = 27
We get two linear equations,
3x + 4y = 18
4.5x + 6y = 27
Multiplying the first equation throughout with 4.5 and the second equation throughout with 3, we get,
13.5x + 18y = 81
13.5x + 18y = 81
Since both the equations coincide, Michael and Ashley bought same amount of Turkey and Ham.
Hence Michael and Ashley bought same amount of turkey and ham.
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Suppose that the relation G is defined as follows Give the domain and range of G Write your answers using set notation. domain- range
Due to the constant value of 0 as well as the leading term 1, the provided polynomial function is a rational function.
An explanation of polynomial functionAn equation's function that only uses ou pas integer exponents or only nonzero multipliers of a variable, as in an equation, quadratic equation, etc., is said to have a polynomial function. A good example is the exponent of the polynomial 2x+5.
Here,
Exponents for the provided polynomial function are positive integers.
The exponent of the positive number 2x is 1.and is a real number with the exponent 5, respectively.
One of the parameters in the function is a real integer like 5, while another is 1.
As a result, the function is described by a polynomial.
It is polynomial because it has a degree of 5.
A polynomial is expressed in standard form by writing the terms in increasing order of words with lower exponents, starting with the term the with highest exponent.
The polynomial has the standard form f(x)=2x+ 1.
consisting of the leading phrase 1 and the constant 0.
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Dante deposits $300 to open a savings account. He will earn 2% interest each year on his
money If he makes no deposits or withdrawals, how much money will Dante earn in interest
in 1 year? How much money will be in the account after 4 years?
When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.
what is amount ?aggregate attempting to determine the whole amount, time, or quantity. The amount at hand or under consideration is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, how much you have, how much you need, or how much you can get. He needs that much money to make ends meet.
given
A= P( 1- rt )
A = 275 ( 1+ 300 )
A = 275( 1.4 )= $385
When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.
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